Question

The angular speed of electron in the nth orbit of hydrogen atom is

Answer 1

We know that the velocity of electron in the $n^{th}$ orbit is $v_n=r_n{\omega }_n$

${\omega }_n=$ angular velocity

${\omega }_n=\frac{v_n}{r_n}$

but $v_n=\frac{z{e}^2}{2{\in }_{o}nn}$

$\Rightarrow {\omega }_n=\frac{z{e}^2}{2{\in }_{o}nn}\propto \frac{1}{r_n}$

$\therefore {\omega }_n\propto \frac{1}{n}$.